Chain snake moves

L fluctuates in time as the chain (or snake) moves. A full description of chain dynamics requires knowledge of the probability distribution of the primitive path lengths. This problem has been solved exactly by Helfand and Pearson in 1983 for a lattice model of a chain in a regular array of... 

All of the characteristics were predicted correctly by the de Gennes theory. These experiments provide significant evidence that polymer chains actually move like snakes through a grass composed of other snakes. 

Figure 8.11. Reptation of a polymer chain. The chain moves snake-like through its confining...

The polymer literature yields a variety of specialized move types in particular for lattice homopolymers [110]. Sampling methods like the slithering snake and reptation algorithms (see ref. Ill and references therein) or the original configurational-bias/chain growth algorithms [112,113] were specifically... 

Reptation theory description of polymer structure is analogous to a bowl of live snakes (Teraoka et al., 1992). In this bowl reside a mesh of entangled, linear flexible polymer chains that continue to wriggle within a minimal range, effectively forming a tube-like structure. It is within this tube that the polymer chains move back and forth and over sufficient periods of time, the polymer chain can actually move along the tube to new interaction sites with fellow polymer chains or other media. 

Extension of this theory can also be used for treating concentrated polymer solution response. In this case, the motion of, and drag on, a single bead is determined by the mean intermolecular force field. In either the dilute or concentrated solution cases, orientation distribution functions can be obtained that allow for the specification of the stress tensor field involved. For the concentrated spring-bead model, Bird et al. (46) point out that because of the proximity of the surrounding molecules (i.e., spring-beads), it is easier for the model molecule to move in the direction of the polymer chain backbone rather than perpendicular to it. In other words, the polymer finds itself executing a sort of a snake-like motion, called reptation (47), as shown in Fig. 3.8(b). 

Fig. 49a. A representative configuration of block copolymers on the lattice (For clarity a square lattice is shown, while all work refers to a simple cubic lattice). Three symmetric diblock copolymers are shown, each of chain length N = 10. The two monomeric species are labeled A-type (full dots) and B-type (open dots). The vacancies are not shown explicitly, but are assumed to reside on each lattice site left unoccupied by either of the two species of monomer. A volume fraction of < >v = 0.2 is used, since experience with blends [107] has shown that such a system behaves like a very dense melt. The energy contributions eAA, eBB and eAB are shown, b Examples of typical slithering-snake [298,299] motion monomer situated at point labelled by 5 is removed, and one of sites 1,2,3 is randomly chosen for occupation. Note that unlike Refs. [298,299] also the junction point needs to be displaced accordingly, as shown in the figure. For the reverse process, monomer at 3 is removed and the sites 4,5,6 are considered for attachment (of course, a move to site 6 is rejected due to excluded volume constraints), c Interchange of A-Block and B-Block of a diblock copolymer chain. From Fried and Binder [325],...

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